Nadia is 20 years older than Ishaan. Twelve years ago, Nadia was 3 times older than Ishaan. How old is Nadia now?
We can use the given information to write down two equations that describe the ages of Nadia and Ishaan. Let Nadia's current age be $n$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $n = i + 20$ Twelve years ago, Nadia was $n - 12$ years old, and Ishaan was $i - 12$ years old. The information in the second sentence can be expressed in the following equation: $n - 12 = 3(i - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to solve our first equation for $i$ and substitute it into our second equation. Solving our first equation for $i$ , we get: $i = n - 20$ . Substituting this into our second equation, we get the equation: $n - 12 = 3($ $(n - 20)$ $ -$ $ 12)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $n - 12 = 3n - 96$ Solving for $n$ , we get: $2 n = 84$ $n = 42$.